"Alright, then I'll be right back." Normally, York would try to offer his patient some comfort, but it was Tarn. By his promise he shouldn't be around the maniac at all. By all logic he shouldn't be trying to help him. This one kindness wouldn't change anything.

He hesitates in getting supplies -- maybe they should just let nature take its course.

No. This is no way to die. York's been watching the Cetagandans suffer and die for days now, he can't commit anyone else that fate on purpose. So he grabs the rest of what he needs and goes back to Tarn to start an IV. He just isn't terribly gentle as he raises a vein in Tarn's arm.